Thanks for that. But you know what they say extraordinary claims require extraordinary evidence. I'm sure if this is ever proven too a sufficient degree they'll have no problem obtaining funding.

Sometimes something extraordinary is also pretty subtle. Why can't even modest results that show something new be extraordinary? Perhaps extraordinary is in the intellectual flexibility of the beholder.

When does a skeptic's evaluation turn to "that's extraordinary?" And is that a sound benchmark to evaluate the merit?

Separating the two photon directions allows them to control their interaction (equivalent of the cavity taper and/or dielectric). In the EMdrive the two directions are intimately coupled within the cavity. If you fold figure 1 in half (vertical fold line) you have something like a tapered microwave cavity. I don't see the need to invoke negative mass (they did say effectively) as the same description looks like the "self accelerating" particle papers.

quasiparticles such as electrons and holes in solid-statecrystals, massspring systems or collective excitations such asBoseEinstein condensates in lattices may exhibit a dispersionrelation with regions of inverted curvature where the effective massis negative. Similarly, in photonic guiding structures, the effectivephoton mass can be positive or negative depending on the sign ofthe associated group velocity dispersion

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This is directly analogous to a relativistic particle whose mass seems to increase during the courseof acceleration and therefore cannot exceed the velocity of light. Thehyperbolic trajectory of a constantly accelerated relativistic particleviewed from an inertial reference frame coincides well with themotion of our optical diametric drive (dashed white line overlaid toFig. 4a,b; see Supplementary Methods), thus proving the ongoingaction of the propulsion mechanism.

Concerning whether they observed defocusing, they state:

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In contrast, when the same Gaussianexcitation excites the lower band (where the effective mass isnegative), the nonlinearity reverses its action and induces strongnonlinear defocusing effects (Fig. 3b).In our set-up, optical diametric drive acceleration is realizedby allowing the self-trapped wave packet of Fig. 3a to nonlinearlyinteract with the defocusing beam shown in Fig. 3b. While thepositive-mass soliton is attracted by the negative-mass beam, thelatter is constantly repelled. As a result, the positive-mass beam willpermanently pursue its negative-mass counterpart while the latterone tries to escape.

Thanks for that. But you know what they say extraordinary claims require extraordinary evidence. I'm sure if this is ever proven too a sufficient degree they'll have no problem obtaining funding.

Sometimes something extraordinary is also pretty subtle. Why can't even modest results that show something new be extraordinary? Perhaps extraordinary is in the intellectual flexibility of the beholder.

When does a skeptic's evaluation turn to "that's extraordinary?" And is that a sound benchmark to evaluate the merit?

Problem is you're trying to convince the scientific & engineering majority and that's a heck of a lot of people you need to satisfy of the validity of your results.

About the ARIADNA study #04/1201 from the ESA, evaluating the anomalous Feigel Process for the extraction of momentum from a vacuum, I quote the conclusions of the final report (emphasis by me):

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On the basis of our study, we come to the following conclusions: The derivation of the generally covariant relativistic constitutive relations for a moving magnetoelectric medium, together with the subsequent analysis of the vacuum waves travelling through the sample of a finite size shows that the magnetoelectric body will not move, despite the presence of a certain asummetry between the left- and right-moving waves in the matter. However, this only refers to the case of waves due to vacuum fluctuation.For the real waves falling symmetrically from the two sides on a magnetoelectric body, we expect a nontrivial effect of the Feigel type. Thus, we cannot confirm the possibility of "extracting momentum from nothing".

So this study pretty much invalidated the anomalous Feigel effect when considering the QFV conjecture, aka "extraction of momentum from the virtual photons of the quantum vacuum fluctuations". It showed however that an anomalous Feigel effect could be obtained with real photons. So for a thruster, does the photons (microwaves ?) generator (magnetron ?) has to be decoupled (exterior) from the thruster or could it be part of it as in an EmDrive?

So the ARIADNA study #04/1201 from the ESA in my view lends credibility to the researchers (which they don't need anyway) and validity to the momentum from the QV approach (referencing van Tiggelen et al) to explaining Emdrive I've remarked on, in that the ESA was willing to throw money at the problem and put mainstream science on contract to figure it out. There's a back story to all this.

I realize that van Tiggelen may not even know what Emdrive is and would likely not want association with it.

The fact is though, that this copper can isn't expelling any reaction mass yet folks are measuring thrust from it. It is crystal clear that in order for this to happen, symmetry must be broken somewhere.Trust me, I didn't stumble onto this because of the name of the paper. I was looking for broken symmetry (parity at the time) and found that it had already been done:http://forum.nasaspaceflight.com/index.php?topic=29276.msg1269010#msg1269010

The Feigel paper, and the work that was inspired by it later on by others, (which is a progression of research spanning a decade) is why I feel this research is important and likely a good candidate to explain the anomalous thrust.

We're aware that the Feigel effect is falsified*. The work that came later from it is what is important. Note that this story begins in 2004. There is a timeline which one must follow in order to make sense of available information. Here's the timeline:

A recent publication [Phys. Rev. Lett. 92, 020404 (2004)] raises the possibility of momentum transfer from zero-point quantum fluctuations to matter, controlled by applied electric and magnetic fields. We present a Lorentz-invariant description using field-theoretical regularization techniques. We find no momentum transfer for homogeneous media, but predict a very small transfer for a Casimir-type geometry.

4)So from there the prospect of gaining momentum from the QV using magnetoelectric matter was dependent on a "Casimir-type geometry." This is remarked about here*, **:http://forum.nasaspaceflight.com/index.php?topic=36313.msg1335771#msg1335771Several years later, others go on to say, that yes you can gain momentum from the QV and non-reciprocity is required, and here's how you can achieve that using a fully quantum approach (as opposed to Feigel's classical approach). That is all the PT symmetry breaking stuff from earlier posts.

So from the research above on magnetoelectrics, you need a Casimir geometry:From what I gather, there are 3 potential areas inside the emdrive which can fit into this metric.1) For the unloaded cavity (no dielectric) the gaps where the end plates meet the frustum. Two Casimir plates in a ring, one large, one small.2) For the loaded cavity, the above, but add in the gap between the copper and HDPE as well as the gap between the two HDPE discs.3) More difficult to justify in my opinion, is the whole cavity technically is a Casimir cavity, albeit a gigantic one.

So it seems like a good idea to sandwich some Cr2O3 in between the two HDPE discs and/or between the HDPE and the copper end plate. That's why I got a baggie of the stuff to eventually try out. I have some .5 micron in powder form and .3 micron in paste form.

Separating the two photon directions allows them to control their interaction (equivalent of the cavity taper and/or dielectric). In the EMdrive the two directions are intimately coupled within the cavity. If you fold figure 1 in half (vertical fold line) you have something like a tapered microwave cavity. I don't see the need to invoke negative mass (they did say effectively) as the same description looks like the "self accelerating" particle papers.

The question is "is the nonlinearity a required condition ?".

I remember reading somewhere that nonlinearity is required. I remember @Rodal saying so too. I'm trying to find the references.*

I didn't know what was going on at the time but after the fact it may have been one of these:Second harmonic generation (SHG), or frequency doubling, generation of light with a doubled frequency (half the wavelength), two photons are destroyed creating a single photon at two times the frequency.Third harmonic generation (THG), generation of light with a tripled frequency (one-third the wavelength), three photons are destroyed creating a single photon at three times the frequency.

Which means that I have to go back and do it again and try and measure the frequency difference.

“PT-symmetry breaking alone is not sufficient to have nonreciprocal response; operation in the nonlinear regime is also necessary. In the linear regime, light transmission is always reciprocal regardless of whether PT-symmetry is broken or not,”

....While the formula I've been using is based on satisfying General Relativity, it does not tell us anything about the mechanism of momentum conservation.. PT asymmetry, as Mulletron mentions, is a viable candidate, and nonlinear frequency effects could (in theory) satisfy the requirement.

Can anybody present quantitative experimentally-measured data showing significant PT asymmetry or nonlinear frequency effects for a bulk High Density Polyethylene (purchased commercially from McMaster Carr, if my memory serves me correctly ?) used as the dielectric by NASA Eagleworks in their tests ?

That could be a Rosetta Stone...

Does it have to be nonlinearity of the dielectric? Why not nonlinearity of the cavity itself?

Well the cavity walls may have thin films of nonlinear material on them, but I'm not entirely convinced that nonlinear behavior is absolutely necessary. The asymmetric behavior of the photon timelines may well be the fundamental factor.

Well the cavity walls may have thin films of nonlinear material on them, but I'm not entirely convinced that nonlinear behavior is absolutely necessary. The asymmetric behavior of the photon timelines may well be the fundamental factor.

I can understand the asymmetry arising from nonlinearity. This paper (a really outstanding contribution by @Mulletron, who really deserves the strongest thank you for posting it)

shows it to arise from a nonlinear (second order) term in a perturbation expansion. @Mulletron had previously posted another paper showing the effect arising from a fourth order term in a perturbation expansion:

On the other hand, if there is no nonlinear behavior in a dielectric insert and there is no nonlinear material in the cavity inner walls, electromagnetic fields can be described by linear Maxwell's equations, and hence we have harmonic electromagnetic fields and standing waves inside the cavity, the Poynting vector will oscillate at a frequency twice as high as the electromagnetic field frequency, and hence if it points towards the small base during a half-period (of the Poynting vector frequency), it will point in the opposite direction towards the big base, during the next half-period. The behavior seems reversible and hence self-cancelling if it can be described by linear Maxwell's equations.

Yes, the question is, if an accelerating frame of reference is intrinsically nonlinear, (for photons along that axis) what transformation can maintain that relationship (ie. potential) in the rest frame. Maxwell's Equations (the tautological relationship between the field and particle descriptions) just won't do it by themselves. Different higher spacial GR scenarios will theoretically generate a gravitational current, but I haven't seen anything convincing.

A structure can be non-reciprocal when biased with a vector that is odd under time reversal, i.e. the magnetic field, the current, the linear momentum and the angular momentum [J. D. Jackson, Classical Electrodynamics, John Wiley & Sons, Inc., 1999].

So from the research above on magnetoelectrics, you need a Casimir geometry:From what I gather, there are 3 potential areas inside the emdrive which can fit into this metric.1) For the unloaded cavity (no dielectric) the gaps where the end plates meet the frustum. Two Casimir plates in a ring, one large, one small.2) For the loaded cavity, the above, but add in the gap between the copper and HDPE as well as the gap between the two HDPE discs.3) More difficult to justify in my opinion, is the whole cavity technically is a Casimir cavity, albeit a gigantic one.

So it seems like a good idea to sandwich some Cr2O3 in between the two HDPE discs and/or between the HDPE and the copper end plate. That's why I got a baggie of the stuff to eventually try out. I have some .5 micron in powder form and .3 micron in paste form.

Regarding 3): Is it thinkable that the EM-drive is a kind of large 'inverse' Casimir cavity? In the 'normal' Casimir cavity, there is a reduced virtual photon spectrum, compared to outside the cavity. However, one might argue that inside the comparably giant EM-drive cavity, there is an increased real photon spectrum for that specific spatial volume, compared to the outside of the cavity and hence a similar effect arises as would be the case for a 'normal' Casimir cavity. Does that make sense?

Casimir effects manifest in boundary areas between two closely spaced objects. I know you thinking in terms of solid materials with microscopic separations. But what about the gaps between lobes of RF in those graphics of the various modes? aren't they boundary interfaces in their own right?

EDIT: Isn't a requirement for casimir set ups spacing of incredibly small dimensions; not just any gap will do. considerable calibration of the gap is a part of experiments on Casimir force and effects.

EDIT: caveat: i recently read an article that had to do with amplification of vacuum energy. but Casimir force normally drops off extremely quickly with distance between plates or spheres.

I would dare say this is the same concept as the phase modulation of the electro-magnetic field for propulsion concept also. I get the impression their negative mass laser is just a laser at a different phase from the other laser so that the effect it induces does negative work.

"Photons excited in the lower band have a negative effective mass, whereas for thosein the upper branch this same quantity is positive." and " The phase relation between the two loops is appropriately set by external phase modulation..." page 787 last quarter

The idea being the 1st wire puts off a signal and light (electric field parallel to the current). The -dB/dt light signal approaches the 2nd wire. If the 2nd wire moves its current the same as the signal from the 1st wire then it does positive work against the light and is attracted (positive beam). If the 2nd wires current moves the opposite as the current appears (light) to be in the 1st wire negative work is done and the wire is repulsed moving the device in the direction of negative work.

The difference being were dealing with lasers and instead of microwaves, visible light. Instead of wires I am guessing were dealing with currents in dielectrics or mediums.

negative work-energy on one side, positive work-energy on the other and a force from one to the other. Again with implications of light being induced to travel in the direction of constructive interference.

(by the way do the resulting photons from constructive interference merge? (frequency doubling) I have been wondering if they do considering how the electric field of light from constructive interference overlaps) I know in some non-linear crystals it can be done with lasers but at a very specific angle. I would guess in the case of the propulsion if it it is a small effect, if at all, but it could lead to high energy radiation if it builds up, maybe. The mention of frequency mixing sounds like it for some reason.

So from the research above on magnetoelectrics, you need a Casimir geometry:From what I gather, there are 3 potential areas inside the emdrive which can fit into this metric.

[snip] 3) More difficult to justify in my opinion, is the whole cavity technically is a Casimir cavity, albeit a gigantic one.

Regarding 3): Is it thinkable that the EM-drive is a kind of large 'inverse' Casimir cavity? In the 'normal' Casimir cavity, there is a reduced virtual photon spectrum, compared to outside the cavity. However, one might argue that inside the comparably giant EM-drive cavity, there is an increased real photon spectrum for that specific spatial volume, compared to the outside of the cavity and hence a similar effect arises as would be the case for a 'normal' Casimir cavity. Does that make sense?

What do you think?

It makes sense but the frustum cavity is so huge compared to a Casimir cavity. The Casimir force doesn't dominate in such a spacious regime.

So from the research above on magnetoelectrics, you need a Casimir geometry:From what I gather, there are 3 potential areas inside the emdrive which can fit into this metric.

[snip] 3) More difficult to justify in my opinion, is the whole cavity technically is a Casimir cavity, albeit a gigantic one.

Regarding 3): Is it thinkable that the EM-drive is a kind of large 'inverse' Casimir cavity? In the 'normal' Casimir cavity, there is a reduced virtual photon spectrum, compared to outside the cavity. However, one might argue that inside the comparably giant EM-drive cavity, there is an increased real photon spectrum for that specific spatial volume, compared to the outside of the cavity and hence a similar effect arises as would be the case for a 'normal' Casimir cavity. Does that make sense?

What do you think?

It makes sense but the frustum cavity is so huge compared to a Casimir cavity. The Casimir force doesn't dominate in such a spacious regime.

Hmm.. I seem to remember that Paul March wrote somewhere in this thread that the Casimir regime shows a 1/r^4 dependency (due to 5 proposed spatial dimensions). I'm just curious whether there is a possibility of existence for a kind of 'pseudo' (or what have you) Casimir effect that shows up in our 3+1 dimensional space for 'real photons' instead of the proposed 5+1 dimensional space for 'virtual photons'. Following the logic of 'n+1 dimensions needed', could there be a Casimir-like regime that shows a 1/r^2 dependency for our 3D-space? Just wondering .

Something that makes me think that time delay phase modulation EM propulsion is going on inside the cavity, [diametric propulsion if you want to call it that] is I remember the big plate being fairly hot like positive work was going on there and the narrow end of the cavity looked fairly cool in comparison (negative work?). If so then propulsion being toward the side doing negative work [the narrow end].

Something that makes me think that time delay phase modulation EM propulsion is going on inside the cavity, [diametric propulsion if you want to call it that] is I remember the big plate being fairly hot like positive work was going on there and the narrow end of the cavity looked fairly cool in comparison (negative work?). If so then propulsion being toward the side doing negative work [the narrow end].

The small base of NASA's Eagleworks EM Drive truncated cone is insulated by the (2.13 inches) thick polymer HDPE while the large base of the truncated cone is not insulated and it is directly exposed to induction heating.

On the other hand, Prof. Juan Yang in China did not use dielectric inserts, and hence neither end of their truncated cone EM Drive was insulated. The temperature at the center of the small end (thermocouple #1) in the Chinese experiment rose much more than the temperature at the center of the big end (thermocouple #6), actually the small end experienced the highest overall temperature in the Chinese EM Drive experiments.

A thought I just had, given that the frustum cavity is a truncated cone and the HDPE is a cylinder, does anyone have any idea how the RF might be effected if the HDPE was converted into a truncated cone such that it's depth into the frustum is the same (2.13 inches), but it actually takes up the entire width with a relatively tight fit?

Thanks for the welcome. I've been around high power RF for many years and have seen low temp PTFE issues at relatively low temps. Specifically, changes in capacitance, yeilding center frequency drift in tchebychev bandpass filters using PTFE tape and discs. Outgassing in hermetically sealed tubes were noticed. Could be totally unrelated but...maybe not.

Agreed, outgassing (due to microwave heating of water vapor previously trapped in the HDPE or PTFE polymer dielectric) would be something to watch out for in a vacuum environment at significantly lower temperatures (near 200 deg F) than pyrolysis (>700 deg F).

This Lawrence Livermore Lab report on outgassing of water vapor from HDPE is pertinent:

It concludes that outgassing of H2O from HDPE can be significantly reduced by vacuum baking at 368 degres K (203 deg F) for a few hours prior to device assembly.

Well put...brings back memories of PTFE baking at 150C overnight. We also noticed other contaminants such as machine oil (circular dielectrics formed with a lathe), oil from parts handler's skin, etc. Might be even more important to clean and shock the dielectrics for vacuum testing.

Something that makes me think that time delay phase modulation EM propulsion is going on inside the cavity, [diametric propulsion if you want to call it that] is I remember the big plate being fairly hot like positive work was going on there and the narrow end of the cavity looked fairly cool in comparison (negative work?). If so then propulsion being toward the side doing negative work [the narrow end].

The small base of NASA's Eagleworks EM Drive truncated cone is insulated by the (2.13 inches) thick polymer HDPE while the large base of the truncated cone is not insulated and it is directly exposed to induction heating.

On the other hand, Prof. Juan Yang in China did not use dielectric inserts, and hence neither end of their truncated cone EM Drive was insulated. The temperature at the center of the small end (thermocouple #1) in the Chinese experiment rose much more than the temperature at the center of the big end (thermocouple #6), actually the small end experienced the highest overall temperature in the Chinese EM Drive experiments.

Thanks for pointing out the difference between the two drives. I notice they both get the same force direction. I am now wondering about the over all thermal energy at the large end compared to the sidewalls and small end together and if they differ overall. The Chinese EM Drive small end may be more hot but it's also a small area compared to the large end. I'll have to look up if the Chinese version is more or less efficient (N/Watt) than the one with the dielectric? This makes me wonder if more negative work would be going on with the dielectric installed making it more efficient.